8.3.3.1 - Example: SAT Scores

Example: SAT Scores Section

This example uses the dataset from Lesson 8.3.3 to walk through the five-step hypothesis testing procedure using the Minitab Express output.

Research question: Do students score differently on the SAT-Math and SAT-Verbal tests?

1. Check assumptions and write hypotheses

Because the sample size is large (\(n \ge 30\)), the t distribution may be used to approximate the sampling distribution.

\(H_{0}:\mu_d=0\)
\(H_{a}:\mu_d \ne 0\)

2. Calculate the test statistic
Test
Null hypothesis H0: \(\mu_d\) = 0
Alternative hypothesis H1: \(\mu_d\) ≠ 0
T-Value P-Value
3.18 0.0017

The t test statistic is 3.18.

3. Determine the p value associated with the test statistic

From the output, the p value is 0.0017

4. Make a decision

\(p\leq .05\), therefore our decision is to reject the null hypothesis

5. State a "real world" conclusion

There is evidence that in the population, on average, students' SAT-Math and their SAT-Verbal scores are different.